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United States Patent |
5,245,552
|
Andersson
,   et al.
|
September 14, 1993
|
Method and apparatus for actively reducing multiple-source repetitive
vibrations
Abstract
A method and apparatus for reducing multiple-source repetitive vibrations
in a region or structure (12) by applying control vibrations to the region
or structure via actuators (18), frequently recalculating the control
vibrations based on source elements to accommodate for varying phase
differences between the sources of the repetitive vibrations (14) and
(16), and cyclically updating the source elements of the control
vibrations is disclosed. The repetitive vibrations are sensed (20)
synchronously with the repetitive vibration source chosen as the reference
source and decomposed into a number of frequency components corresponding
to the reference source. The control vibrations are formed of the same
frequency components and applied synchronously with the reference source.
Each frequency component of the control vibrations is defined by source
elements, one for cancelling vibrations produced by each of the repetitive
vibration sources. A first estimate of the source elements of the
frequency components, defining control vibrations that will reduce the
sensed vibrations, is made. The source elements of the frequency
components and the phase differences between the reference source and the
other repetitive vibration sources are used to calculate control signals
that drive the actuators ( 18) that produce the control vibrations. The
control signals are frequently recalculated using the instantaneous phase
differences. Cyclically, the source elements of the frequency components
of the control vibrations are updated to improve the reduction of the
sensed vibrations. The updated source elements are used to frequently
recalculate the control signals driving the actuators based upon the
instantaneous phase differences between the reference source and the other
repetitive vibration sources.
Inventors:
|
Andersson; Anders O. (Seattle, WA);
Godo; Erik L. (Kirkland, WA)
|
Assignee:
|
The Boeing Company (Seattle, WA)
|
Appl. No.:
|
608971 |
Filed:
|
October 31, 1990 |
Current U.S. Class: |
700/280; 381/71.12; 381/71.2 |
Intern'l Class: |
G01M 007/00; G01H 017/00 |
Field of Search: |
364/507,508,574,551.02,581
381/71
73/602,625,645-648
416/34
|
References Cited
U.S. Patent Documents
4122303 | Oct., 1978 | Chaplin et al. | 179/1.
|
4153815 | May., 1979 | Chaplin et al. | 179/1.
|
4417098 | Nov., 1983 | Chaplin et al. | 381/94.
|
4435751 | Mar., 1984 | Hori et al. | 364/574.
|
4449235 | May., 1984 | Swigert | 381/71.
|
4473906 | Sep., 1984 | Warnaka et al. | 381/71.
|
4477505 | Oct., 1984 | Warnaka | 428/160.
|
4480333 | Oct., 1984 | Ross | 381/71.
|
4489441 | Dec., 1984 | Chaplin | 381/71.
|
4490841 | Dec., 1984 | Chaplin et al. | 381/71.
|
4525791 | Jun., 1985 | Hagiwara et al. | 364/508.
|
4527282 | Jul., 1985 | Chaplin et al. | 381/71.
|
4562589 | Dec., 1985 | Warnaka et al. | 381/71.
|
4566118 | Jan., 1986 | Chaplin et al. | 381/71.
|
4589133 | May., 1986 | Swinbanks | 381/71.
|
4596033 | Jun., 1986 | Swinbanks | 381/71.
|
4600863 | Jul., 1986 | Chaplin et al. | 318/114.
|
4626730 | Dec., 1986 | Hubbard, Jr. | 310/326.
|
4654871 | Mar., 1987 | Chaplin et al. | 381/72.
|
4669122 | May., 1987 | Swinbanks | 381/71.
|
4689821 | Aug., 1987 | Salikuddin et al. | 381/71.
|
4715559 | Dec., 1987 | Fuller | 244/1.
|
4736431 | Apr., 1988 | Allie et al. | 381/71.
|
4947435 | Aug., 1990 | Taylor | 381/71.
|
Foreign Patent Documents |
0252647 | Jan., 1988 | EP.
| |
WO88/02912 | Apr., 1988 | WO.
| |
2187063A | Aug., 1987 | GB.
| |
2191063A | Dec., 1987 | GB.
| |
Other References
Taylor, R. B., P. E. Zwicke, P. Gold and W. Miao, "Analytical Design and
Evaluation of an Active Control System for Helicopter Vibration Reduction
and Gust Response Alleviation", NASA, Jul. 1980.
|
Primary Examiner: Cosimano; Edward R.
Assistant Examiner: Pipala; E.
Attorney, Agent or Firm: Christensen, O'Connor, Johnson & Kindness
Claims
The embodiments of the invention in which an exclusive property or
privilege is claimed are defined as follows:
1. A method of reducing vibrations in a region or structure, the vibrations
being produced by multiple sources of repetitive vibrations, said method
comprising the steps of:
(a) applying control vibrations at a plurality of first locations in a
region or structure, said control vibrations created from sets of
control-vibration frequency components so that each of said control
vibrations is created from one of said sets of control-vibration frequency
components, each of said control-vibration frequency components composed
of source elements for cancelling vibrations produced by multiple sources
of repetitive vibrations; and
(b) cyclically updating said control vibrations by:
(i) determining the phase difference between a reference signal and a
source signal, said source signal being derived from a first source, said
first source being one of said multiple sources of repetitive vibrations;
and
(ii) updating said sets of control-vibration frequency components based on
said phase difference and said source elements.
2. The method claimed in claim 1, wherein said step of updating said sets
of control-vibration frequency components comprises the substeps of:
(a) weighting each of the source elements of each of the control-vibration
frequency components with factors including said phase difference; and
(b) calculating an updated amplitude and phase pair for each of said
control-vibration frequency components by forming a sum including the
weighted source elements corresponding to the control-vibration frequency
component whose amplitude and phase pair is being updated.
3. The method claimed in claim 2, wherein said phase difference represents
the time integral of the difference between the frequency of said
reference signal and said source signal.
4. The method claimed in claim 3, wherein said step of applying control
vibrations comprises the substeps of:
(a) inverse-decomposing said sets of control-vibration frequency components
to obtain control-vibration control signals; and
(b) using said control-vibration control signals to create the control
vibrations in said region or structure.
5. The method claimed in claim 4, wherein each of said sets of
control-vibration frequency components contains frequency components
corresponding to the fundamental frequency of said reference signal and
harmonics thereof.
6. The method claimed in claim 5, wherein said control vibrations are
applied synchronously with said reference signal.
7. The method claimed in claim 6, wherein said source signal forms a first
source signal and including the step of determining the phase difference
between said reference signal and a second source signal, said second
source signal being derived from a second source, said second source being
one of said multiple sources of repetitive vibrations, and wherein each of
said control-vibration frequency components is composed of two source
elements according to the following equation:
a.sub. (n)=Q.sub.11 (n)e.sup.jn.phi. 1+R.sub. (n)e.sup.jn.phi. 2
where:
a.sub. (n) is a complex number representing the amplitude and phase of a
frequency component of the set of control-vibration frequency components
of the control-vibration applied at a particular first location identified
by the subscript, .sub.
n is an integer equal to the harmonic number of said frequency component;
.phi..sub.1 is the phase difference between said first source signal and
said reference signal and .phi..sub.2 is the phase difference between said
second source signal and said reference signal; and
Q.sub. (n) and R.sub. (n) are complex numbers representing the source
elements of said frequency component, wherein Q.sub. (n) is the source
element corresponding to said first source and R.sub. (n) is the source
element corresponding to said second source.
8. The method claimed in claim 7, wherein said source elements are
periodically updated by:
(a) sensing vibrations at a plurality of second locations in said region or
structure;
(b) determining representative values of said .phi..sub.1 and .phi..sub.2
phase differences based on the values of the .phi..sub.1 and .phi..sub.2
phase differences determined while said vibrations are being sensed at
said plurality of second locations;
(c) decomposing said sensed vibrations into sets of sensed-vibration
frequency components;
(d) calculating updates for the source elements of selected frequency
components of said sets of control-vibration frequency components, said
updates based on said sets of sensed-vibration frequency components and
said representative values of said .phi..sub.1 and .phi..sub.2 phase
differences; and
(e) updating the source elements by updating the source elements of said
selected frequency components of said sets of control-vibration frequency
components based on said calculated updates.
9. The method claimed in claim 8, wherein said step of calculating updates
for the source elements of selected frequency components of said sets of
control-vibration frequency components comprises:
(a) transforming frequency components of said sets of sensed-vibration
frequency components into updates for said selected frequency components
of said sets of control-vibration frequency components; and
(b) calculating source element updates based on said frequency component
updates and said representative values of said .phi..sub.1 and .phi..sub.2
phase differences.
10. The method claimed in claim 9, wherein said source elements of the
selected frequency components of said sets of control-vibration frequency
components are updated by adding said source element updates to the
present values of the corresponding source elements according to the
following equations:
.DELTA.Q.sub. (n)+Q.sub. (n).fwdarw.Q.sub. (n)
.DELTA.R.sub. (n)+R.sub. (n).fwdarw.R.sub. (n)
where:
Q.sub. (n) and R.sub. (n) are the complex numbers representing the source
elements of a frequency component of the set of control-vibration
frequency components of the control-vibration applied at a particular
first location identified by the subscript, , wherein Q.sub. (n) is the
source element corresponding to said first source and R.sub. (n) is the
source element corresponding to said second source; and
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n) are complex numbers representing
the updates for said source elements, wherein .DELTA.Q.sub. (n) is the
update for said source element Q.sub. (n), and .DELTA.R.sub. (n) is the
update for said source element R.sub. (n).
11. The method claimed in claim 10, wherein the source element updates are
calculated by solving the following matrix equation in a weighted
least-squares sense:
##EQU3##
where: .gamma..sub.1 and .gamma..sub.2 are scalars;
.phi..sub.1 is said representative value of the phase difference between
said first source signal and said reference signal;
.phi..sub.2 is said representative value of the phase difference between
said second source signal and said reference signal;
.DELTA.a.sub. (n) is a complex number representing the amplitude and phase
update for a frequency component of the set of control-vibration frequency
components of the control vibration applied at a particular first location
identified by the subscript, ;
n is an integer equal to the harmonic number of said frequency component;
and
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n) are the updates for the source
elements of said frequency component.
12. The method claimed in claim 11, wherein said second source signal forms
said reference signal.
13. The method claimed in claim 11 or 12, wherein said step of decomposing
said sensed vibrations comprises performing a Fast Fourier Transformation
on each of said sensed vibrations.
14. The method claimed in claim 13, wherein said step of
inverse-decomposing said sets of control-vibration frequency components
comprises performing an inverse Fast Fourier Transformation on each of
said sets of control-vibration frequency components.
15. The method claimed in claim 14, wherein the frequency components of
each of said sets of sensed-vibration frequency components are the same as
the frequency components of each of said sets of control-vibration
frequency components.
16. The method claimed in claim 15, wherein said sensed vibrations are
sensed synchronously with said reference signal.
17. The method claimed in claim 16, wherein said selected frequency
components of said sets of control-vibration frequency components are
selected by:
(a) determining the magnitude of the frequency components of said sets of
sensed-vibration frequency components based on selected criteria; and
(b) selecting those frequency components that have the greatest magnitude,
the number of selected frequency components selected being less than the
number of frequency components in said sets of control-vibration frequency
components.
18. The method claimed in claim 1, wherein said source elements are
periodically updated by:
(a) sensing vibrations at a plurality of second locations in said region or
structure;
(b) determining a representative value of said phase difference between
said reference signal and said source signal based on the values of said
phase difference determined while said vibrations are being sensed at said
plurality of second locations;
(c) decomposing said sensed vibrations into sets of sensed-vibration
frequency components;
(d) calculating updates for the source elements of selected frequency
components of said sets of control-vibration frequency components, said
updates based on said sets of sensed-vibration frequency components and
said representative value of said phase difference; and
(e) updating the source elements by updating the source elements of said
selected frequency components of said sets of control-vibration frequency
components based on said calculated updates.
19. The method claimed in 18, wherein said step of calculating updates for
the source elements of selected frequency components of said sets of
control-vibration frequency components comprises:
(a) transforming frequency components of said sets of sensed-vibration
frequency components into updates for said selected frequency components
of said sets of control-vibration frequency components; and
(b) calculating source element updates based on said frequency component
updates and said representative value of said phase difference.
20. The method claimed in claim 19, wherein said source elements of the
selected frequency components of said sets control-vibration frequency
components are updated by summing said source element updates with the
present values of the corresponding source elements.
21. The method claimed in claim 20, wherein said phase difference
represents the time integral of the difference between the frequency of
said reference signal and said source signal.
22. The method claimed in claim 21, wherein said source signal forms a
first source signal and including the step of determining the phase
difference between said reference signal and a second source signal, said
second source signal being derived from a second source, said second
source being one of said multiple sources of repetitive vibrations, and
wherein each of said control-vibration frequency components is composed of
two source elements, one for each of said first and second sources of
repetitive vibrations.
23. The method claimed in claim 22, wherein said source element updates are
calculated by solving the following matrix equation in a weighted
least-squares sense:
##EQU4##
where: .gamma..sub.1 and .gamma..sub.2 are scalars;
.phi..sub.1 is said representative value of the phase difference between
said first source signal and said reference signal;
.phi..sub.2 a representative value of the phase difference between said
second source signal and said reference signal based on the values of the
phase difference between said second source signal and said reference
signal determined while said vibrations are being sensed at said plurality
of second locations;
.DELTA.a.sub. (n) is a complex number representing the amplitude and phase
update of a frequency component of the set of control-vibration frequency
components of the control vibration applied at a particular first location
identified by the subscript, .sub. ;
n is an integer equal to the harmonic number of said frequency component;
and
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n) are complex numbers representing
the updates for the source elements of said frequency component, wherein
.DELTA.Q.sub. (n) is the update for the source element Q.sub. (n)
corresponding to said first source, and .DELTA.R.sub. (n) is the update
for the source element R.sub. (n) corresponding to said second source.
24. The method claimed in claim 23, wherein said step updating said sets of
control-vibration frequency components comprises the steps of:
(a) weighting each of the source elements of each of the control-vibration
frequency components with factors including the corresponding phase
differences; and
(b) calculating an updated amplitude and phase pair for each of said
control-vibration frequency components by forming a sum including the
weighted source elements corresponding to the control-vibration frequency
component whose amplitude and phase pair is being updated.
25. The method claimed in claim 24, wherein said step of applying control
vibrations comprises the steps of:
(a) inverse-decomposing said sets of control-vibration frequency components
to obtain control-vibration control signals; and
(b) using said control-vibration control signals to create said control
vibrations in said region or structure.
26. The method claimed in claim 25, wherein each of said sets of
control-vibration frequency components contains frequency components
corresponding to the fundamental frequency of said reference signal and
harmonics thereof.
27. The method claimed in claim 26, wherein said control vibrations are
applied synchronously with said reference signal.
28. An apparatus for reducing vibrations in a region or structure, the
vibrations being produced by multiple sources of repetitive vibrations,
said apparatus comprising:
(a) phase differentiator means for determining the phase difference between
a reference signal and a source signal, said source signal based on a
first source, said first source being one of multiple sources of
repetitive vibrations that produce vibrations in a region or structure;
(b) a plurality of actuators for applying control vibrations at a plurality
of first locations in said region or structure; and
(c) output means coupled to said plurality of actuators and said phase
differentiator means for:
(i) applying drive signals to said plurality of actuators, said drive
signals created from sets of control-vibration frequency components so
that each of said drive signals is created from one of said sets of
control-vibration frequency components, each of said control-vibration
frequency components composed of source elements for cancelling the
vibrations produced by said multiple sources of repetitive vibrations; and
(ii) cyclically updating said control vibrations by:
(1) receiving said phase difference determined by said phase differentiator
means; and
(2) updating said sets of control-vibration frequency components based on
said phase difference and said source elements.
29. The apparatus claimed in claim 28, wherein said output means includes
an inverse-decomposition means for producing control-vibration control
signals by inverse-decomposing said sets of control-vibration frequency
components, and wherein said output means synchronously creates said drive
signals from said control-vibration control signals.
30. The apparatus claimed in claim 29, wherein said phase differentiator
means includes:
(a) sensor means coupled to said first source for monitoring said first
source and producing said source signal, the frequency of said source
signal being based on the fundamental frequency of said first source;
(b) synchronized signal generating means coupled to said sensor means for:
(i) receiving said source signal produced by the sensor means; and
(ii) producing a synchronized signal having a frequency that is a multiple
of the frequency of said source signal and is synchronized therewith; and
(c) a phase differentiator coupled to said synchronized signal generating
means for:
(i) receiving said synchronized signal;
(ii) determining said phase difference between said reference signal and
said source signal by analyzing the phase difference between said
synchronized signal and said reference signal; and
(iii) applying said phase difference determined by analysis to said output
means.
31. The apparatus claimed in claim 30, wherein said updated sets of
control-vibration frequency components are formed by:
(a) weighting each of the source elements of each of the control-vibration
frequency components with factors including said phase difference between
said reference signal and said source signal; and
(b) calculating an updated amplitude and phase pair for each of said
control-vibration frequency components by forming a sum including the
weighted source elements corresponding to the control-vibration frequency
component whose amplitude and phase pair is being updated.
32. The apparatus claimed in claim 31, wherein the phase difference
determined by said phase differentiator represents the time integral of
the difference between the frequency of said reference signal and the
frequency of said source signal.
33. The apparatus claimed in claim 32, wherein each of said sets of
control-vibration frequency components contains frequency components
corresponding to the fundamental frequency of said reference signal and
harmonics thereof.
34. The apparatus claimed in claim 33, wherein said drive signals are
synchronized with said reference signal.
35. The apparatus claimed in claim 34, wherein said synchronized signal
forms a first synchronized signal and said source signal forms a first
source signal and wherein said sensor means includes means coupled to a
second source, said second source being one of said multiple sources of
repetitive vibrations, said means for monitoring said second source and
producing a second source signal whose frequency is based on the
fundamental frequency of said second source, and wherein said synchronized
signal generating means includes means for receiving said second source
signal and producing a second synchronized signal having a frequency that
is a multiple of the frequency of said second source signal and is
synchronized therewith, and wherein said phase differentiator receives
said second synchronized signal and determines the phase difference
between said second source signal and said reference signal by analyzing
the phase difference between said second synchronized signal and said
reference signal, and wherein each of said control-vibration frequency
components is composed of two source elements according to the following
equation:
a.sub. (n)=Q.sub. (n)e.sup.jn.phi. 1+R.sub. (n)e.sup.jn.phi. 2
where:
a.sub. (n) is a complex number representing the amplitude and phase of a
frequency component of the set of control-vibration frequency components
of the control-vibration applied by a particular actuator identified by
the subscript, .sub. ,
n is an integer equal to the harmonic number of said frequency component;
.phi..sub.1 is the phase difference between said first source signal and
said reference signal;
.phi..sub.2 is the phase difference between said second source signal and
said reference signal; and
Q.sub. (n) and R.sub. (n) are complex numbers representing the source
elements of said frequency component, Q.sub. (n) is the source element
corresponding to said first source and R.sub. (n) is the source element
corresponding to said second source.
36. The apparatus claimed in claim 35, further comprising:
(a) a plurality of sensors for sensing vibrations at a plurality of second
locations in said region or structure;
(b) decomposition means coupled to said plurality of sensors for receiving
and decomposing said sensed vibrations into sets of sensed-vibration
frequency components; and
(c) controller means coupled to said decomposition means, said phase
differentiator, and said output means for:
(i) receiving said sets of sensed-vibration frequency components from said
decomposition means;
(ii) receiving from said phase differentiator means representative values
of said .phi..sub.1 and .phi..sub.2 phase differences determined while
said sensors are sensing the vibrations that are decomposed by said
decomposition means;
(iii) calculating updates for the sources elements of selected frequency
components of said sets of control-vibration frequency components, said
updates based on said sets of sensed-vibration frequency components and
said representative values of said .phi..sub.1 and .phi..sub.2 phase
differences;
(iv) updating the source elements by updating the source elements of said
selected frequency components of said sets of control-vibration frequency
components based on said calculated updates; and
(v) supplying said updated source elements to said output means.
37. The apparatus claimed in claim 36, wherein said updates for the source
elements of selected frequency components of said sets of
control-vibration frequency components are calculated by:
(a) transforming frequency components of said sets of sensed-vibration
frequency components into updates for said selected frequency components
of said sets of control-vibration frequency components; and
(b) calculating source element updates based on said frequency component
updates and said representative values of said .phi..sub.1 and .phi..sub.2
phase differences.
38. The apparatus claimed in claim 37, wherein said source elements of the
selected frequency components of said sets of control-vibration frequency
components are updated by adding said source element updates to the
present values of the corresponding source elements according to the
following equations:
.DELTA.Q.sub. (n)+Q.sub. (n).fwdarw.Q.sub. (n)
.DELTA.R.sub. (n)+R.sub. (n).fwdarw.R.sub. (n)
where:
Q.sub. (n) and R.sub. (n) are the complex numbers representing the source
elements of a frequency component of the set of control-vibration
frequency components of the control-vibration applied by a particular
actuator identified by the subscript , wherein Q.sub. (n) is the source
element corresponding to said first source and R.sub. (n) is the source
element corresponding to said second source; and
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n) are complex numbers representing
the updates for said source elements, wherein .DELTA.Q.sub. (n) is the
update for said source element Q.sub. (n), and .DELTA.R.sub. (n) is the
update for said source element R.sub. (n).
39. The apparatus claimed in claim 38, wherein the source element updates
are calculated by solving the following matrix equation in a weighted
least-squares sense:
##EQU5##
where: .gamma..sub.1 and .gamma..sub.2 are scalars;
.phi..sub.1 is the representative value of the phase difference between
said first source signal and said reference signal;
.phi..sub.2 is the representative value of the phase difference between
said second source signal and said reference signal;
.DELTA.a.sub. (n) is a complex number representing the amplitude and phase
update for a frequency component of the set of control-vibration frequency
components of the control vibration applied by a particular actuator
identified by the subscript, ;
n is an integer equal to the harmonic number of said frequency component;
and
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n) are the updates for the source
elements of said frequency component.
40. The apparatus claimed in claim 39, wherein said second synchronized
signal forms said reference signal.
41. The apparatus claimed in claim 39 or 40, wherein said decomposition
means includes digital signal processor means programmed to perform Fast
Fourier Transforms and said inverse-decomposition means includes digital
signal processor means programmed to perform inverse Fast Fourier
Transforms.
42. The apparatus claimed in claim 41, wherein the frequency components of
each of said sets of sensed-vibration frequency components are the same as
the frequency components of each of said sets of control-vibration
frequency components.
43. The apparatus claimed in claim 42, wherein said selected frequency
components of the sets of control-vibration frequency components are
selected by:
(a) determining the magnitude of the frequency components of said sets of
sensed-vibration frequency components based on selected criteria; and
(b) selecting those frequency components that have the greatest magnitude,
the number of frequency components selected being less than the number of
frequency components in said sets of control-vibration frequency
components.
44. The apparatus claimed in claim 28, further comprising:
(a) a plurality of sensors for sensing vibrations at a plurality of second
locations in said region or structure;
(b) decomposition means coupled to said plurality of sensors for receiving
and decomposing said sensed vibrations into sets of sensed-vibration
frequency components; and
(c) controller means coupled to said decomposition means, said phase
differentiator means, and said output means for:
(i) receiving said sets of sensed-vibration frequency components from said
decomposition means;
(ii) receiving from said phase differentiator means a representative value
of said phase difference between said reference signal and said source
signal based on the values of the phase difference between said reference
signal and said source signal while said sensors are sensing the
vibrations that are decomposed by said decomposition means;
(iii) calculating updates for the source elements of selected frequency
components of said sets of control-vibration frequency components, said
updates based on said sets of sensed-vibration frequency components and
said representative value of said phase difference;
(iv) updating the source elements by updating the source elements of said
selected frequency components of said sets of control-vibration frequency
components based on said calculated updates; and
(v) supplying said updated source elements to said output means.
45. The apparatus claimed in claim 44, wherein said updates for the source
elements of selected frequency components of said sets of
control-vibration frequency components are calculated by:
(a) transforming frequency components of said sets of sensed-vibration
frequency components into updates for said selected frequency components
of said sets of control-vibration frequency components; and
(b) calculating source element updates based on said frequency component
updates and said representative value of said phase difference.
46. The apparatus claimed in claim 45, wherein said source elements of the
selected frequency components of said sets of control-vibration frequency
components are updated by summing said source element updates with the
present values of the corresponding source elements.
47. The apparatus claimed in claim 46, wherein said phase difference
represents the time integral of the difference between the frequency of
said reference signal and the frequency of said source signal.
48. The apparatus claimed in claim 47, wherein said source signal forms a
first source signal and wherein said phase differentiator means determines
the phase difference between said reference signal and a second source
signal, said second source signal based on a second one of said multiple
sources of repetitive vibrations, further wherein said control-vibrations
frequency components are composed of two source elements, one for each of
said first and second source of repetitive vibrations.
49. The apparatus claimed in claim 48, wherein said source element updates
are calculated by solving the following matrix equation in a weighted
least-squares sense:
##EQU6##
where: .gamma..sub.1 and .gamma..sub.2 are scalars;
.phi..sub.1 is said representative value of the phase difference between
said first source signal and said reference signal;
.phi..sub.2 is a representative value of the phase difference between said
second source signal and said reference signal, said .phi..sub.2
representative value based on the values of the phase difference between
said second source signal and said reference signal while said sensors are
sensing the vibrations that are decomposed by said decomposition means;
.DELTA.a.sub. (n) is a complex number representing the amplitude and phase
update of a frequency component of the set of control-vibration frequency
components of the control vibration applied by a particular actuator
identified by the subscript, ;
n is an integer equal to the harmonic number of said frequency component;
and
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n) are complex numbers representing
the updates for the source elements of said frequency component, wherein
.DELTA.Q.sub. (n) is the update for the source element corresponding to
said first source, and .DELTA.R.sub. (n) is the update for the source
element corresponding to said second source.
50. The apparatus claimed in claim 49, wherein said output means includes
an inverse-decomposition means for producing control-vibration control
signals by inverse-decomposing said sets of control-vibration frequency
components, and wherein said output means synchronously creates said drive
signals from said control-vibration control signals.
51. The apparatus claimed in claim 50, wherein said phase differentiator
means includes:
(a) sensor means coupled to said first and second sources of repetitive
vibrations for monitoring said first and second sources and producing said
first and second source signals each of whose frequency is based on the
fundamental frequency generated by the related source;
(b) synchronized signal generating means coupled to said sensor means for
producing synchronized signals, said synchronized signal generating means:
(i) receiving the first and second source signals produced by the sensor
means; and
(ii) producing for said first and second source signals, related first and
second synchronized signals each having a frequency that is a multiple of
the frequency of the related source signal and is synchronized therewith;
and
(c) a phase differentiator coupled to said synchronized signal generating
means for:
(i) receiving said first and second synchronized signals;
(ii) determining said phase differences between said reference signal and
said first and second source signals by analyzing the phase differences
between said reference signal and said first and second synchronized
signals; and
(iii) applying said phase differences determined by analysis to said output
means and said controller means.
52. The apparatus claimed in claim 51, wherein said updated sets of
control-vibration frequency components are formed by:
(a) weighting each of the source elements of each of the control-vibration
frequency components with factors including the corresponding phase
differences between said reference signal and said first and second source
signals; and
(b) calculating an updated amplitude and phase pair for each of said
control-vibration frequency components by forming a sum including the
weighted source elements corresponding to the control-vibration frequency
component whose amplitude and phase is being updated.
53. The apparatus claimed in claim 52, wherein each of said sets of
control-vibration frequency components contains frequency components
corresponding to the fundamental frequency of said reference signal and
harmonics thereof.
54. The apparatus claimed in claim 53, wherein said drive signals are
synchronized with said reference signal.
Description
TECHNICAL AREA
This invention is directed to methods and apparatus for reducing repetitive
vibrations and, more particularly, to methods and apparatus for actively
reducing multiple-source repetitive vibrations.
BACKGROUND OF THE INVENTION
Various methods and apparatus have been proposed for actively reducing
vibrations in a region containing a gas or liquid or in a structure of
solid bodies. The concept of actively reducing vibrations consists of
introducing control vibrations to combine with vibrations in a region or
structure so that the resultant vibrations in the region or structure are
of a lower amplitude than the vibrations in the region or structure
without the control vibrations. The active reduction of audible noise in a
region has been particularly pursued, e.g., the reduction of noise in an
aircraft cabin generated by jet or propeller engines. Actively reducing
vibrations is of considerable importance for low-frequency vibrations
because of the difficulty in passively reducing low-frequency components.
Passive reduction typically refers to the use of vibration absorbing or
blocking materials such as sound absorbing liners in the case of noises in
gases. The amount of such vibration absorbing materials needed to be
effective increases considerably as the frequency of the vibration is
decreased and, thus, is impractical in applications where weight and
volume are constrained.
Recently, devices that reduce vibrations in a region or structure by
sensing vibrations in the region or structure, decomposing the sensed
vibrations into frequency components, calculating output frequency
components with some frequency-domain operation, composing control
vibrations from the output frequency components, and applying the control
vibrations in the region or structure via actuators to reduce the sensed
vibrations have been introduced. Generally referred to herein as
frequency-domain vibration controllers, such a controller, for example, is
disclosed in U.S. patent application Ser. No. 07/575,223, filed Aug. 30,
1990, entitled "Method and Apparatus for Actively Reducing Repetitive
Vibrations" by Anders O. Andersson et al. and assigned to the assignee of
the present application.
Frequency-domain vibration controllers reduce repetitive vibrations
produced by one or more repetitive vibration sources by performing a
frequency-domain operation on a present cycle of the sensed vibrations to
determine control vibrations and introducing the control vibrations at a
later cycle of the sensed vibrations. The control vibrations reduce the
sensed vibrations, which consist of the repetitive vibrations introduced
by the repetitive vibration sources and the control vibrations introduced
by the actuators. The control vibrations can be cyclically updated to
increase the amount of reduction.
Current frequency-domain vibration controllers may be used to reduce
repetitive vibrations created by multiple sources of repetitive
vibrations. Generally, the operation of frequency-domain vibration
controllers is synchronized with one of the repetitive vibration sources,
referred to herein as the reference source. The repetitive vibrations in
the region or structure are sensed synchronously with the reference
source, and the control vibrations are applied to the region or structure
synchronously with the reference source. Generally, the sensed vibrations
are decomposed into frequency components consisting of a fundamental
frequency and harmonics thereof. The fundamental frequency of the
decomposition is chosen to be the fundamental frequency of the reference
source. A frequency-domain vibration controller operating synchronously
with a reference source can effectively reduce the repetitive vibrations
produced by multiple sources of repetitive vibrations if all sources of
repetitive vibrations operate at exactly the same frequency. However,
there are applications in which there are multiple sources of repetitive
vibrations operating at slightly different frequencies. In these
applications, the slight differences in the frequencies of the sources
produce vibrational beats that are not reduced by the frequency-domain
vibration controller.
Take, for example, the application of a frequency-domain vibration
controller for reducing the noise in an aircraft cabin generated by the
aircraft's jet engines. Prior art frequency-domain vibration controllers
used in aircraft were operated synchronously with the rotational frequency
of one of the aircraft's jet engines, i.e., the chosen reference source.
However, the jet engines of an aircraft rarely operate at exactly the same
rotational frequency. Therefore, each jet engine produces a repetitive
vibration of a slightly different frequency. The differences in the
frequencies of the repetitive vibrations produce vibrational beats that
are not effectively reduced by the frequency-domain vibration controller.
These vibrational beats are annoying to the passengers of the aircraft.
The present invention improves prior art frequency-domain vibration
controllers such that these controllers can more effectively reduce
repetitive vibrations generated by sources operating at slightly different
frequencies. In essence, a frequency-domain vibration controller operating
in accordance with the present invention operates synchronously with the
repetitive vibration source chosen as the reference source, but frequently
corrects the control vibrations based upon the instantaneous phase
differences between the sources of the repetitive vibrations.
Generally, in frequency-domain vibration controllers, the control
vibrations are cyclically updated to approach waveforms that optimize the
reduction of the repetitive vibrations in the region or structure. In
addition, some frequency-domain vibration controllers incorporate an
adaptive method of updating the control vibrations. Such adaptive methods
effectively optimize the reduction of the sensed vibrations whether or not
changes are occurring in the repetitive vibrations, the region or
structure, or the frequency-domain vibration controller. The method of the
present invention can be used with such adaptive frequency-domain
vibration controllers. Further, the method of the present invention is
adaptive itself.
SUMMARY OF THE INVENTION
In accordance with this invention, a method and apparatus for reducing
multiple-source repetitive vibrations in a region or structure by applying
a plurality of control vibrations to the region or structure via
actuators, frequently recalculating the control vibrations based on source
elements to accommodate varying phase differences between the sources of
the repetitive vibrations, and cyclically updating the source elements of
the control vibrations is provided. One of the plurality of repetitive
vibration sources is chosen as the reference source. The phase differences
between the reference source and the other repetitive vibration sources
are monitored. The repetitive vibration at each of a plurality of
locations in the region or structure is sensed synchronously with the
reference source. Each sensed vibration is decomposed into a number of
frequency components corresponding to the frequency components of the
repetitive vibrations produced by the reference source. The control
vibrations are formed of the same frequency components and are applied
synchronously with the reference source. Each frequency component of the
control vibrations is defined by a plurality of source elements, one for
controlling vibrations produced by each of the repetitive vibration
sources. An estimate of the source elements of each control vibration's
frequency components, defining control vibrations that will reduce the
sensed vibrations, is made. The source elements of the control-vibration
frequency components along with the phase differences between the
reference source and the other sources are used to calculate control
signals that are used to drive the actuators, which as a result produce
the control vibrations. The control signals are frequently recalculated
using the instantaneous phase differences between the reference source and
the other sources. Cyclically, the source elements of the control
vibration frequency components are updated to improve the reduction of the
sensed vibrations. Each update cycle is begun by sensing, synchronously
with the reference source, the vibration at each of the plurality of
locations in the region or structure at which a sensor is located. Each
sensed vibration is decomposed into the same frequency components as
before. The frequency components with the greatest amplitude are selected
for updating. For each control vibration the source elements of the
selected frequency components are updated. The control signals are then
frequently recalculated using the updated source elements and the
instantaneous phase differences.
In accordance with further aspects of the invention, the source elements of
the control vibration frequency components are adaptively updated so as to
improve the accuracy of the decomposition of the frequency components into
source elements, whether or not changes occur in the repetitive
vibrations, the region or structure, or the apparatus used to carry out
the method of the invention. The source elements are adaptively updated in
the update cycle. For each control vibration, amplitude and phase updates
are calculated for the frequency components selected for updating. The
amplitude and phase updates are decomposed into source element updates
based upon the phase differences between the reference source and the
other repetitive vibration sources. The source element updates are added
to the present source elements to obtain updated source elements.
The preferred form of an apparatus formed in accordance with the invention
includes: a plurality of sensors, an input system, a controller, an output
system, a plurality of actuators, a plurality of synchronized signal
generators, and a phase differentiator. The sensors and actuators are
dispersed in the region or structure. Signals produced by the sensors are
applied to the input system. The input system is coupled to the
controller, and the controller is coupled to the output system. The
actuators are coupled to the output system. A synchronized signal
generator is provided for each repetitive vibration source. Preferably,
each synchronized signal generator includes a low-pass filter and a
phase-locked loop. The input of the low-pass filter is coupled to the
corresponding repetitive vibration source via a sensor monitoring the
source, and the output of the low-pass filter is coupled to the input of
the phase-locked loop. One of the repetitive vibration sources is
designated as the reference source. The output of the synchronized signal
generator coupled to the reference source is applied to the input system,
the controller, and the output system. The output from each synchronized
signal generator is coupled to the phase differentiator, and the output of
the phase differentiator is applied to the controller and output system.
In operation, the input system samples the analog input signals produced
by the sensors to produce corresponding digital input signals. The
sampling is synchronized by the synchronized signal produced by the
synchronized signal generator coupled to the reference source. The input
system decomposes the digital input signals into a set of frequency
components. The controller selects the frequency components to be updated,
calculates source element updates, and updates the source elements
therewith. Using the source elements and the instantaneous phase
differences produced by the phase differentiator, the output system
frequently calculates amplitudes and phases for the control-vibration
frequency components. The output system inverse decomposes the amplitudes
and phases to form digital control signals. The output system converts the
digital control signals to analog control signals and simultaneously
applies the analog control signals to the inputs of the actuators. The
digital-to-analog conversion is synchronized by the synchronized signal
corresponding to the reference source.
As will be appreciated from the foregoing brief summary, a method and
apparatus for reducing multiple-source repetitive vibrations in a region
or structure by applying a plurality of control vibrations to the region
or structure via actuators, frequently recalculating the control
vibrations based on source elements to accommodate for the varying phase
differences between the sources of the repetitive vibrations, and
cyclically updating the source elements of the control vibrations is
provided. The method and apparatus of the present invention can control
repetitive vibrations produced by a plurality of repetitive vibration
sources operating at slightly different frequencies. The differences in
the frequencies of the sources are accommodated by frequently
recalculating the control vibrations using the instantaneous phase
differences between a reference source and the other repetitive vibration
sources. The source elements used to calculate the control vibrations are
cyclically updated in an adaptive manner so as to improve the reduction of
the sensed vibrations whether or not changes are occurring in the
repetitive vibrations, the region or structure, or the apparatus used to
carry out the method of the invention.
It will be further appreciated that prior art frequency-domain vibration
controllers can be modified in accordance with the present invention to
obtain frequency-domain vibration controllers that can control
multiple-source repetitive vibrations. Generally, prior art
frequency-domain vibration controllers can only control repetitive
vibrations produced by a single source or multiple sources operating at
exactly the same frequency. If modified to produce a frequency-domain
vibration controller in accordance with the present invention, prior art
frequency-domain vibration controllers can control repetitive vibrations
produced by multiple sources operating at slightly different frequencies.
As in the prior art, a frequency-domain vibration controller according to
the present invention operates synchronously with a single source of the
repetitive vibrations. However, in accordance with the invention, the
phase and frequency of each repetitive vibration source is monitored and
the control vibrations are frequently recalculated to accommodate the
varying phase differences between the repetitive vibration sources.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing objects and many of the attendant advantages of this
invention will become more readily appreciated as the same becomes better
understood by reference to the following detailed description when taken
in conjunction with the accompanying drawings, wherein:
FIG. 1 is a simplified block diagram of an apparatus according to the
invention for actively reducing multiple-source repetitive vibrations;
FIG. 2 is a simplified flow diagram illustrating a prior art method of
operating frequency-domain vibration controllers;
FIG. 3 is a flow diagram illustrating a method according to the invention
of recalculating control vibrations based upon phase differences between
the repetitive vibration sources;
FIGS. 4A and 4B form a composite flow diagram illustrating a method
according to the invention of updating source elements of the control
vibrations; and
FIG. 5 is a block diagram of an alternative embodiment of a portion of the
apparatus illustrated in FIG. 1.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 1 is a simplified block diagram of an apparatus formed in accordance
with the invention for actively reducing multiple-source repetitive
vibrations in a region or structure 12. The method and apparatus of the
invention can be used to effectively reduce repetitive vibrations produced
by a plurality of repetitive vibration sources that differ slightly in
frequency. For simplicity, the apparatus shown in FIG. 1 and the methods
according to the invention shown in the succeeding figures describe an
application in which there are two repetitive vibration sources operating
at slightly different frequencies. It will be understood that the
apparatus and method can be used to reduce repetitive vibrations produced
by more than two repetitive vibration sources operating at slightly
different frequencies.
Two representative vibration sources 14 and 16 produce repetitive
vibrations in the region or structure 12. The purpose of the apparatus is
to reduce the amplitude of the so-produced repetitive vibrations in the
region or structure 12 because such vibrations are undesirable. The
apparatus includes a plurality of actuators 18 that introduce control
vibrations in the region or structure 12 to oppose the repetitive
vibrations in the region or structure 12 produced by the sources 14 and
16. The control vibrations generated by the actuators 18 are dependent on
the vibrations sensed by a plurality of sensors 20 located in the region
or on the structure. The apparatus includes a multi-input/multi-output
(MIMO) feedback control system 22 that cyclically updates source elements,
of which the control vibrations are composed, so as to minimize the sensed
vibrations. The MIMO feedback control system 22 includes an input system
24, a controller 26 that receives the output of the input system 24, and
an output system 28 that receives the output of the controller 26. The
input system 24 receives the output of each region/structure sensor 20,
and the output system 28 calculates control signals using the source
elements calculated by the controller 26 and drives the actuators 18 with
these signals.
One of the repetitive vibration sources 14 is chosen as the reference
source and the operation of the MIMO feedback control system 22 is
synchronized with this source 14. A synchronized signal generator 29 that
includes a low-pass (LP) filter 30 and a phase-locked loop 32 monitors the
reference source 14 via a reference sensor 34. The output of the
phase-locked loop 32 is a synchronized signal that is applied to the input
system 24 and the output system 28 to synchronize the operation of these
systems with the reference source 14. The synchronized signal generated by
the phase-locked loop 32 is also fed to the controller 26 to define the
frequency of the repetitive vibrations produced by the reference source
14. The repetitive vibration source 16 is monitored by another
synchronized signal generator 35, which also includes a low-pass (LP)
filter 36 and a phase-locked loop 38, via another sensor 40. The output of
both the phase-locked loop 32 and the phase-locked loop 38 are input to a
phase differentiator 42. Phase differentiator 42 determines the phase
difference between the repetitive vibrations produced by the other source
16 and the reference source 14. The phase difference between the
repetitive vibrations produced by the other source 16 and the reference
source 14 varies with time because the other source 16 and the reference
source 14 differ slightly in frequency. The phase differentiator 42
determines the instantaneous phase difference between the repetitive
vibrations produced by the other source 16 and the repetitive vibrations
produced by the reference source 14. The phase difference determined by
the phase differentiator 42 is applied to the controller 26 and to the
output system 28. The controller 26 uses the phase difference when
calculating new source elements that compose the control vibrations. The
output system 28 frequently recalculates control signals that drive the
actuators to produce the control vibrations. The control signals are
composed of two sets of source elements, one for controlling the
vibrations produced by the reference source 14 and the other for
controlling the vibrations produced by the other source 16. The control
signals are frequently recalculated to accommodate for the varying phase
difference between the sources.
Take, for example, application of the invention for the reduction of
repetitive noise in the passenger cabin of a jet aircraft. In this
example, the region or structure 12 is the gaseous region of the passenger
cabin, and the repetitive vibrations are repetitive noises generated by
the jet engines of a twin-jet aircraft, i.e., the reference source 14 and
the other source 16 are the jet engines of the aircraft. An apparatus
according to the invention reduces the repetitive noise to, among other
things, improve the comfort of passengers. Further in this example, the
actuators 18 are preferably loudspeakers, and the region/structure sensors
20 are preferably microphones. Both loudspeakers and microphones are
preferably dispersed throughout the passenger cabin, and preferably the
number of sensors is greater than the number of actuators. Without these
preferred characteristics of actuator/sensor placement and actuator/sensor
numbers, the MIMO feedback control system 22 may produce control
vibrations that completely reduces the sensed vibrations at each sensor,
but result in no appreciable reduction of the repetitive vibrations in the
regions between the sensors. Still further in this example, the reference
sensor 34 and the other sensor 40 are preferably tachometers respectively
monitoring the rotational frequency of the reference source 14 and the
other source 16 (jet engines). The jet engines have slightly different
rotational frequencies, and thus produce repetitive vibrations of slightly
different frequency. The frequency difference can be modeled as a
time-varying phase between the jet engines. The input system 24,
controller 26, and output system 28 are preferably on-board electronic
devices including digital processors. The low-pass filters 30 and 36, the
phase-locked loops 32 and 38, and the phase differentiator 42 are also
preferably on-board electronic devices.
It will be appreciated that the invention can be used in various other
applications to reduce repetitive vibrations. In such other applications,
the majority of the devices of the frequency-domain vibration controller
could be the same electronic devices. However, the choice of sensors and
actuators will depend on the application. For example, if the invention is
used to reduce repetitive vibrations in a structure that consists of an
electronic transformer, the region/structure sensors 20 would preferably
be accelerometers and the actuators 18 would preferably be shakers; both
accelerometers and shakers would be attached to the transformer.
The synchronized signal generators 29 and 35 monitor the frequency and
phase of the repetitive vibrations produced respectively by the reference
source 14 and the other source 16. As mentioned previously, the
synchronized signal generator 29 includes a low-pass (LP) filter 30 and a
phase-locked loop 32. The reference sensor 34 generates a reference signal
which is applied to the low-pass filter 30 and the output of the low-pass
filter 30 is applied to the phase-locked loop 32. The reference
phase-locked loop 32 produces a synchronized signal that is applied to the
phase differentiator 42, the input system 24, the controller 26, and the
output system 28. The reference signal produced by the reference sensor 34
is filtered by the low-pass filter 30 to remove any high frequencies in
the reference signal that could erroneously trigger the phase-locked loop
32. Similarly, the synchronized signal generator 35 includes the low-pass
(LP) filter 36 and the phase-locked loop 38. The sensor 40 coupled to the
other source 16 generates a reference signal which is applied to the
low-pass filter 36, and the output of the low-pass filter 36 is applied to
the phase-locked loop 38. The output of the phase-locked loop 38 is
applied to the phase differentiator 42.
The difference between the frequency of the repetitive vibrations produced
by the other source 16 and the frequency of the repetitive vibrations
produced by the reference source 14 is modeled as a time-varying phase
difference. The phase differentiator 42 determines this phase difference
based upon the inputs from the synchronized signal generators 29 and 35.
The reference source 14 produces repetitive vibrations having a frequency
f.sub.14 and the other source 16 produces repetitive vibrations of
frequency f.sub.16 (fundamental frequencies). In applications the
invention is directed to, the frequencies f.sub.14 and f.sub.16 are
slightly different and may vary with time. The difference in frequencies
is modeled as a phase difference .phi. as defined in the following
equation:
.phi.=2.pi..intg.(f.sub.16 -f.sub.14)dt (1)
Equation (1) will be recognized to be a time integral of the difference in
the frequency of the other source 16 and reference source 14. The phase
difference .phi. produced by the phase differentiator 42 is applied to the
controller 26 and the output system 28. If there were more than two
repetitive vibration sources, say for example, three repetitive vibration
sources, the apparatus according to the invention would include a third
synchronized signal generator. The phase differentiator would determine
the phase difference between the third source and the reference source 14,
in addition to determining the phase difference between the other source
16 and the reference source 14. Both phase differences would be fed to the
controller 26 and to the output system 28. If additional repetitive
vibration sources existed, similar modifications would be made for the
additional sources.
FIG. 1 shows the MIMO feedback control system 22 in simplified block
diagram form. The MIMO feedback control system 22 is shown to include the
input system 24, the controller 26, and the output system 28. Preferred
components of the input system 24, the controller 26, and the output
system 28 are described in U.S. patent application Ser. No. 07/577,223,
referenced more fully above, which is incorporated herein by reference.
The frequency-domain vibration controller described in said United States
Patent Application has an input system comprised of bandpass filters, a
sampling system, an input memory, and a digital signal processor. The
controller of the frequency-domain vibration controller includes a central
memory and a master processor, and the output system includes an output
memory, an output sequencer, low-pass filters, and a digital signal
processor.
Excluding the phase differentiator 42, synchronized signal generator 35,
and the other sensor 40, the apparatus shown in FIG. 1 is preferably the
same as the prior art frequency-domain vibration controller described in
U.S. patent application Ser. No. 07/575,223 and except for the
modification discussed herein, its method of operation is the same. In
order to avoid unduly complicating the description of the present
invention only a brief description of a frequency-domain vibration
controller of the type described in the foregoing patent application is
presented herein. The description assumes that either the other repetitive
vibration source 16 operates at exactly the same frequency as the
reference repetitive vibration source 14 or the other repetitive vibration
source 16 does not exist. As shown in FIG. 2, the system is first
initialized by performing a start-up sequence resulting in the application
of control vibrations in the region or structure 12, followed by the
periodic execution of an update cycle in which the control vibrations are
updated. The update cycle consists of sensing the sensed vibrations,
decomposing the sensed vibrations, calculating frequency component
updates, updating the frequency components, and inverse-decomposing the
frequency components to obtain new control signals with which to drive the
actuators.
During the start-up sequence, the input system 24 samples the analog signal
produced by each sensor 20 for a plurality of discrete times to produce
digital input signals corresponding to the vibration sensed at each sensor
location. The input system 24 decomposes the digital input signals into a
set of frequency components S by performing a Fast Fourier Transformation
(FFT) on each digital input signal. The amplitudes and phases determined
by the FFT are passed to the controller 26. In response, the controller 26
calculates amplitudes and phases for the frequency components of set S to
be used to compose the control vibrations. The amplitudes and phases for
the control vibrations are stored in the form of complex numbers in the
controller 26. The complex numbers are denoted output complex amplitudes
a.sub. (n), where identifies a specific actuator and n identifies a
specific frequency component. The output complex amplitudes a.sub. (n) are
passed to the output system 28. The output system 28 inverse-decomposes
the output complex amplitudes a.sub. (n) corresponding to the th actuator
by performing an inverse FET. The result of each inverse FET is a digital
control signal a.sub. (t.sub.k) corresponding to the th actuator and is
stored in the output system 28. The output system 28 converts each digital
control signal a.sub. (t.sub.k) to an analog control signal a.sub. (t) and
simultaneously applies the analog control signals a.sub. (t) to the
corresponding actuators. In response to the applied signal, each actuator
generates a corresponding control vibration. Thereafter, each control
vibration is cyclically updated to improve the reduction of the sensed
vibrations.
The update cycles are similar to the initialization start-up sequence. The
input system 24 samples the sensed vibrations to produce digital input
signals. The input system 24 then decomposes each digital input signal by
performing FETs. The resulting amplitudes and phases are used by the
controller 26 to calculate frequency component updates. The frequency
component updates are complex numbers used to update the output complex
amplitudes a.sub. (n). The frequency component updates are denoted output
complex amplitude updates .DELTA.a.sub. (n). The output complex amplitude
updates .DELTA.a.sub. (n) are added to the corresponding output complex
amplitudes a.sub. (n) to update the output complex amplitudes a.sub. (n).
To conclude the update cycle, the output complex amplitudes a.sub. (n),
only some of which may have been updated, are inverse-decomposed by
performing inverse FFTs, producing new digital control signals a.sub.
(t.sub.k). The new digital control signals replace the digital control
signals currently stored in the output system 28. The next update cycle is
then performed in the same manner.
The frequency-domain vibration controller described in the foregoing patent
application operates synchronously with the reference repetitive vibration
source 14. The input system 24 samples the sensed vibrations at discrete
times synchronized with the reference source 14 via a synchronized signal
produced by the phase-locked loop 32. The phase-locked loop 32 produces a
synchronized signal that is synchronized with the repetitive vibrations
produced by the reference source 14 and consists of several pulses per
period of the repetitive vibrations produced by the reference source 14.
The pulses of the synchronized signal trigger the sampling of the input
system 24. Further, the input system 24 decomposes the digital input
signals, resulting from sampling of the sensed vibrations, into a set S of
frequency components. The frequency components of set S are preferably the
fundamental frequency of the repetitive vibrations produced by the
reference source 14 and the first (N-1) harmonics thereof. The fundamental
frequency of the repetitive vibrations produced by the reference source 14
is defined by the phase-locked loop 32. The synchronized signal consists
of a constant number of pulses per period of the repetitive vibrations
produced by the reference source 14. By counting the number of pulses for
some period of time, the frequency of the repetitive vibrations can be
determined. Still further, the controller 26 calculates output complex
amplitudes a.sub. (n) for the frequency components of set S, and the
output system inverse-decomposes the output complex amplitudes a.sub. (n)
to obtain digital control signals a.sub. (t.sub.k). The output system 28
sequences through the digital control signals a.sub. (t.sub.k)
synchronously with the reference source 14; the digital control signals
a.sub. (t.sub.k) are converted to analog signals at times corresponding to
the pulses of the synchronized signal produced by the phase-locked loop
32.
Because the frequency-domain controller operates synchronously with the
reference source 14, the frequency-domain vibration controller is not able
to effectively reduce repetitive vibrations in the region or structure 12
if there are repetitive vibration sources, in addition to the reference
source 14, which produce repetitive vibrations of different frequencies.
The present invention modifies the frequency-domain vibration controller
described in the foregoing patent application in a manner that allows the
controller to effectively reduce repetitive vibrations produced by
multiple repetitive vibration sources operating at slightly different
frequencies. While the present invention is being discussed with reference
to the frequency-domain vibration controller described in the foregoing
patent application, it is to be understood that the invention can be used
to enhance other types of frequency-domain vibration controllers to
achieve the same end result.
As mentioned previously, FIG. 1 shows an apparatus according to the present
invention. The other repetitive vibration source 16 is monitored by the
other sensor 40 and the synchronized signal generator 35. The phase
differentiator 42 determines the phase difference, .phi., between the
repetitive vibrations produced by other source 16 and the reference source
14, as defined in Equation (1). The phase-locked loop 38 produces a signal
synchronized with the repetitive vibrations produced by the other source
16 and consisting of a constant number of pulses per period of the
repetitive vibrations produced by the other source 16. Preferably, the
synchronized signals produced by phase-locked loop 38 and phase-locked
loop 32 consist of the same number of pulses per period of the repetitive
vibrations produced by the sources 16 and 14, respectively. Then,
preferably, the phase differentiator 42 receives the synchronized signals
produced by phase-locked loops 38 and 32, accumulates the number of pulses
in each synchronized signal, and determines the phase difference, .phi.,
based upon the difference in the number of pulses as shown in the
following equation:
.phi.=2.pi.(I.sub.16 -I.sub.14)/I (2)
I.sub.16 and I.sub.14 are respectively the number of pulses accumulated
from the synchronized signals produced by the phase-locked loops 38 and
32, and I is the number of pulses per period of the repetitive vibrations
produced by both sources. The frequency-domain vibration controller shown
in FIG. 1 is operated synchronously with the reference source 14. The
controller 26 and the output system 28 use the phase difference, .phi., to
adjust the control vibrations so that the repetitive vibrations produced
by the combination of the reference source 14 and the other source 16 are
effectively reduced in the region or structure 12.
The flow diagram in FIG. 3 illustrates the preferred method of operation of
the output system 28 to accommodate the phase difference between the
sources 16 and 14. Briefly, each output complex amplitude a.sub. (n) is
composed of a source element for cancelling vibrations produced by the
reference source 14 and a source element for cancelling vibrations
produced by the other source 16. The output complex amplitudes a.sub. (n)
are calculated using the source elements and the instantaneous phase
difference. All of the output complex amplitudes are calculated for the
most recently determined phase difference. The output complex amplitudes
are then inverse-decomposed to obtain digital control signals a.sub.
(t.sub.k). The digital control signals are then stored in the output
system and are used to generate the control vibrations. Subsequently, the
phase difference, .phi., is again determined. The output complex
amplitudes are then recalculated using this present phase difference. The
recalculated output complex amplitudes are then inverse-decomposed to
obtain new digital control signals which replace the previously used
digital control signals. This process of recalculating the digital control
signals is repetitively applied and is explained in detail with reference
to FIG. 3 in the following paragraphs.
The process of FIG. 3 is started by determining the present phase
difference between the other source 16 and the reference source 14. The
digital control signal corresponding to each actuator is sequentially
recalculated based upon the present phase difference. is initialized to
1, and the digital control signal a.sub. (t.sub.k) is recalculated after
recalculating each output complex amplitude a.sub. (n) corresponding to
the th actuator. n is initialized to 1, and the output complex amplitude
a.sub. (n) is recalculated according to the following equation:
a.sub. (n)=Q.sub. (n)+R.sub. (n)e.sup.jn.phi. (3)
In Equation (3) and hereinafter, Q.sub. (n) and R.sub. (n) are complex
numbers representing the source elements corresponding to the reference
source 14 and the other source 16, respectively. Further, e is the natural
logarithm base, j is the square root of -1, and .phi. is the phase
difference. As mentioned previously, a.sub. (n) is the output complex
amplitude corresponding to the nth frequency component of the digital
control signal applied to the th actuator. Each output complex amplitude
a.sub. (n) has two corresponding source elements Q.sub. (n) and R.sub.
(n). A preferred method of calculating the source elements Q.sub. (n) and
R.sub. (n) is presented hereinafter.
In Equation (3), the factor e.sup.jn.phi. incorporates the phase difference
n.phi. between the nth frequency component of the sensed vibration
produced by the other source 16 and the nth frequency component of the
sensed vibration produced by the reference source 14. .phi. is the phase
difference between the fundamental frequency component of the sensed
vibrations produced by the other source 16 and the reference source 14,
and n.phi. is the phase difference between the nth frequency component of
the sensed vibrations produced by the other source 16 and the reference
source 14. This will be readily understood by those skilled in the signal
processing art since n is the harmonic number of the frequency component.
After the output complex amplitude a.sub. (n) is calculated, the result is
stored. Until all frequency components are processed for the th actuator,
n is sequentially incremented by 1 and the output complex amplitude a.sub.
(n) is recalculated for the nth frequency component in the same manner.
After all frequency components have been processed for the th actuator,
the set of complex amplitudes (a.sub. (1), a.sub. (2), . . . , a.sub. (N))
are inverse-decomposed by performing an inverse FET to obtain a new
digital control signal a.sub. (t.sub.k). The new digital control signal
a.sub. (t.sub.k) replaces the digital control signal currently stored in
the output system 28 to drive the th actuator. If all actuators have not
been processed, is incremented by 1 and the digital control signal
a.sub. (t.sub.k) corresponding to the next actuator is recalculated in the
same manner. This process is sequentially repeated until all digital
control signals are recalculated, i.e., all actuators are processed. After
processing all actuators, the entire process is again repeated for a new
phase difference .phi.. In this manner, the digital control signals are
frequently recalculated to accommodate for the time-varying phase
difference .phi. between the source 16 and the reference source 14.
While the process illustrated in FIG. 3 recalculates control signals to
accommodate the difference in the frequency of two sources, it will be
appreciated that the process can be used for any number of sources
differing in frequency. For example, if there were a third source
producing repetitive vibrations in the region or structure 12, then the
composition of the output complex amplitude a.sub. (n) would include a
third source element multiplied by a factor including the phase difference
between the third source and the reference source 14.
The source elements Q.sub. (n) and R.sub. (n) are cyclically updated with
an update cycle. Between updates of the source elements, the digital
control signals are frequently recalculated based upon the source elements
and the instantaneous phase difference determined before each
recalculation of the digital control signals. FIGS. 4A-B form a flow
diagram illustrating a preferred method of updating the source elements.
The process shown in FIGS. 4A-B is similar to the method of operation of
the previously referred-to frequency-domain vibration controller, which
was described with reference to FIG. 2. Specifically, the last three steps
(updating of the frequency components, inverse-decomposing the frequency
components, and replacing the control signals) are modified by the present
invention to accommodate for the frequency difference between the sources.
As will be better understood from the following description, FIGS. 4A-B
illustrate the entire process of updating the source elements, rather than
being limited to the modifications of the last three steps shown in FIG.
2. In FIGS. 4A-B the method of updating the source elements is shown in
detail. The other steps, which have been previously discussed with
reference to the method shown in FIG. 2, are shown at a higher level.
These steps are described in greater detail in U.S. patent application
Ser. No. 07/575,223, which has been incorporated herein by reference.
Before beginning the update cycles, the system is initialized with a
start-up sequence. Preferably, the start-up sequence is similar to the
start-up sequence of the frequency-domain controller discussed above with
reference to FIG. 2. In the start-up sequence, first estimates of the
source elements Q.sub. (n) and R.sub. (n) are determined and the output
system uses the source elements to sequentially recalculate control
signals as shown in FIG. 3. Subsequently, the source elements are
cyclically updated as described in the following paragraphs with reference
to FIGS. 4A-B.
The update cycle is begun by sampling the sensed vibrations and then
decomposing the sensed vibrations into the N frequency components of set
S, as described previously for the frequency-domain vibration controller.
During the sampling of the sensed vibrations, the instantaneous phase
difference, .phi., will vary constantly if there is a difference between
the frequency of the reference source 14 and the other source 16. A
representative value of the phase difference during the sampling of the
sensed vibrations is needed. Preferably, the instantaneous phase
difference determined at the time when the sampling of the sensed
vibrations is half completed is used as the representative value. However,
the phase difference, .phi., determined at different times, for example,
at the beginning of sampling the sensed vibrations could be used as the
representative value, or the average value of the phase difference during
the sampling of the sensed vibrations could be determined and used.
Preferably, the next step comprises forming a subset B of the set S of
frequency components, with the subset B having fewer frequency components
than the set S. The subset B can be formed, for example, by selecting the
frequency components of set S that have the largest sensed vibration
magnitude. The source elements corresponding to the frequency components
of subset B are then updated as described in the following paragraphs.
Only the frequency components of subset B are updated during an update
cycle so that the update cycle is relatively fast, as described in detail
in U.S. patent application Ser. No. 07/575,223, incorporated herein by
reference.
After forming the subset B of frequency components, updates are calculated
for the output complex amplitudes a.sub. (n). The output complex amplitude
updates .DELTA.a.sub. (n) can be calculated using either of the methods
described in the U.S. patent application Ser. No. 07/575,223. It is to be
understood that the updates .DELTA.a.sub. (n) can be calculated with
methods other than those disclosed therein without departing from the
spirit of the present invention.
The source elements corresponding to the frequency components of subset B
are sequentially updated for each actuator. is initialized to 1. The
source elements of the frequency components of subset B are sequentially
updated for the th actuator. n is initialized to the first element of the
subset B. Source element updates .DELTA.Q.sub. (n) and .DELTA.R.sub. (n)
are calculated by solving the following overdetermined set of equations in
a weighted least-squares sense:
##EQU1##
.DELTA.a.sub. (n) is an output complex amplitude update determined in the
previous step of calculating updates for the output complex amplitudes.
.gamma..sub.1 and .gamma..sub.2 are scalar factors, which can have
different values for each combination of and n. .phi. is the
representative value of the phase difference between the other source 16
and the reference source 14.
The matrix Equation (4) represents three linear equations with two
unknowns, .DELTA.Q.sub. (n) and .DELTA.R.sub. (n), and therefore the
system of equations represents an overdetermined set of equations. Since
the matrix Equation (4) represents an overdetermined set of equations, the
matrix equation is solved in a weighted least-squares sense. Solving
overdetermined equations in a weighted least-squares sense is well known
to those skilled in the linear algebra art. The larger the factors
.gamma..sub.1 and .gamma..sub.2 are chosen, the smaller the source element
updates .DELTA.Q.sub. (n) and .DELTA.R.sub. (n) will be and, as a result,
the slower the source elements Q.sub. (n) and R.sub. (n) will change. The
source elements are updated by adding the source element updates to the
corresponding source elements, i.e., .DELTA.Q.sub. (n) is added to Q.sub.
(n), and .DELTA.R.sub. (n) is added to R.sub. (n). If all elements of the
subset B have not been processed, n is set equal to the next element of
subset B, and source element updates are calculated for the nth frequency
component of the digital control signal a.sub. (t.sub.k) corresponding to
the th actuator. This process is sequentially repeated until all
frequency components of subset B are processed for the th actuator. After
processing all frequency components of subset B for the th actuator, is
incremented by 1 and the source elements of the th actuator are updated
in the same manner. This entire process is repeated until all actuators
have been processed, e.g., the source elements of each digital control
signal a.sub. (t.sub.k) are updated.
After the source elements are updated, the update cycle is completed. The
next update cycle, consisting of the same steps, is begun as shown in FIG.
4A. The process of recalculating the digital control signals a.sub.
(t.sub.k), illustrated in FIG. 3 and discussed previously herein, utilizes
the updated source elements.
While FIGS. 4A-B illustrate a preferred method of updating the source
elements, it will be appreciated that other methods of updating the source
elements could be used without departing from the spirit of the invention.
For example, the steps of the update cycle shown in FIG. 4A could be
executed twice before recalculating the source elements. The result would
be two values for each output complex amplitude update .DELTA.a.sub. (n)
and two corresponding values for the phase difference, .phi.. The two
values for the output complex amplitude update .DELTA.a.sub. (n) and the
two values for the phase difference could be combined to form two linear
equations (of the form of Equation 3) in the source element updates
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n). These equations could then be
solved for the source element updates .DELTA.Q.sub. (n) and .DELTA.R.sub.
(n).
As a further alternative method of updating the source elements, input
complex amplitudes resulting from decomposing the sensed vibrations could
be decomposed into source elements and the resulting input source elements
could be transformed into updates for the source elements of the output
complex amplitudes. As previously described, the sensed vibrations are
decomposed into the N frequency components of set S, which correspond to
the frequency components of the reference source 14. The results of the
decompositions are preferably input complex amplitudes p.sub.m (n). For a
particular m and n, the input complex amplitude p.sub.m (n) represents the
amplitude and phase of the nth frequency component of the vibration sensed
at the mth sensor. In applications the present invention is directed to,
the fundamental frequencies f.sub.14 and f.sub.16 of the repetitive
vibration sources 14 and 16 are close in value. As a result, the input
complex amplitudes p.sub.m (n) for a particular n represent the nth
frequency component of the vibrations produced by the other source 16 as
well as the nth frequency component of the vibrations produced by the
reference source 14. However, because the other source 16 operates at a
slightly different frequency than the reference source 14, the input
complex amplitudes p.sub.m (n) vary with time. It follows that the
corresponding output complex amplitudes a.sub. (n) must vary with time to
effectively reduce the nth frequency component of the sensed vibrations.
Preferably, as described previously, the input complex amplitudes p.sub.m
(n) are transformed by a frequency-domain operation to obtain output
complex amplitude updates .DELTA.a.sub. (n). Further in the preferred
method of operation, the output complex amplitude updates .DELTA.a.sub.
(n) are decomposed into source element updates .DELTA.Q.sub. (n) and
.DELTA.R.sub. (n), which are then used to update the source elements
Q.sub. (n) and R.sub. (n) of the output complex amplitudes. Still further
in the preferred method of operation, the output source elements Q.sub.
(n) and R.sub. (n) are then used to frequently recalculate output complex
amplitudes to accommodate for the frequency difference between the other
source 16 and the reference source 14, e.g., to effectively reduce the
time varying input complex amplitudes p.sub.m (n).
However, if the input complex amplitudes p.sub.m (n) are decomposed into
input source elements X.sub.m (n) and Y.sub.m (n), then these input source
elements could be transformed into output source element updates
.DELTA.Q.sub. (n) and .DELTA.R.sub. (n). The transformation of the input
source elements could be accomplished in manners similar to the
transformation of the input complex amplitudes p.sub.m (n) into output
complex amplitude updates .DELTA.a.sub. (n), i.e., using transfer function
matrices as discussed in the U.S. patent application Ser. No. 07/575,223,
incorporated herein by reference.
The input source elements would be defined by the following equation:
p.sub.m (n)=X.sub.m (n)+Y.sub.m (n)e.sup.jn.phi. (5)
The input source elements could be recalculated each update cycle with a
process similar to that shown in FIG. 4B. The resulting input source
elements X.sub.m (n) and Y.sub.m (n) would then be transformed into output
source element updates .DELTA.Q.sub. (n) and .DELTA.R.sub. (n). The update
cycle would be completed by updating the output source elements Q.sub. (n)
and R.sub. (n) with the updates.
As a still further alternative method of operation of a frequency-domain
vibration controller according to the present invention, the
frequency-domain vibration controller could be, and may preferably be,
synchronized at some reference frequency other than the frequency of
either of the sources of repetitive vibrations. For example, the
frequency-domain vibration controller could operate at a reference
frequency f that is the average of the frequencies f.sub.14 and f.sub.16
of the sources 14 and 16. In this example, the repetitive vibrations would
be sensed synchronously at the reference frequency f, and the control
vibrations would be applied synchronously at the reference frequency f.
The sensed vibrations would be decomposed into frequency components
corresponding to the reference frequency f and multiples thereof. The
control vibrations would be composed of the same frequency components. The
output complex amplitudes a.sub. (n) would be decomposed into source
elements. The source elements would then be used to frequently recalculate
the output complex amplitudes using the following equation:
a.sub. (n)=V.sub. (n)e.sup.jn.phi. 14+W.sub. (n)e.sup.jn.phi. 16(6)
In Equation (6), .phi..sub.14 represents the phase difference resulting
from the difference between the frequency of one source 14 and the
reference frequency f, and similarly, .phi..sub.16 represents the phase
difference resulting from the difference between the frequency of the
other source 16 and the reference frequency f. In this alternative method,
the output complex amplitudes would be recalculated as shown in FIG. 3
using Equation (6). The source elements V.sub. (n) and W.sub. (n) could be
updated with a method similar to the method shown in FIGS. 4A-B, Equation
(7), which follows, would be used in place of Equation (4).
##EQU2##
FIG. 5 is a block diagram of a portion of the apparatus shown in FIG. 1
modified in accordance with this alternative method of operation. The
apparatus shown in FIG. 5 produces the reference frequency f and
determines the phase differences .phi..sub.14 and .phi..sub.16. The
modifications include the addition of a voltage divider 44 and a
voltage-controlled oscillator (VCO) 46. The low-pass filters 30 and 36 and
the phase-locked loops 32 and 38 of the synchronized signal generators 29
and 35, and the phase differentiator 42 are also shown in FIG. 5 for ease
of understanding. Subcomponents of the phase-locked loops are also
illustrated in FIG. 5. More specifically, each phase-locked loop 32 and 38
is illustrated as including a voltage-controlled oscillator (VCO) 48, a
frequency divider 50 and a multiplier 52, the typical components of a
phase-locked loop. The outputs of the low-pass filters 30 and 36 are
connected to first inputs of the related multipliers 52. The outputs of
the multipliers 52 are connected to the voltage control inputs of the VCOs
48, and the synchronized signal outputs of the VCOs 48 are connected
through the frequency dividers 50 to the other inputs of the multipliers
52.
As noted above, the output of the low-pass filters 30 and 36 are reference
signals based upon the repetitive vibration sources 14 and 16, i.e., the
reference signals have frequencies f.sub.14 and f.sub.16. The outputs of
the VCOs 48 are synchronized signals that, as a result of the feedback
loop formed by the frequency dividers 50, are synchronized with the
reference signals associated with the sources 14 and 16. The synchronized
signal produced by one VCO 48 has a frequency .alpha.f.sub.14, i.e., a
multiple of the frequency f.sub.14 and the synchronized signal produced by
the other VCO 48 has a frequency of .alpha.f.sub.16, i.e., a multiple of
the frequency f.sub.16. The VCOs 48 also produce DC voltages that are
proportional to the frequencies .alpha.f.sub.14 and .alpha.f.sub.16.
The DC voltages produced by the VCOs of the phase-locked loops 32 and 38
are applied to the voltage divider 44. The voltage divider 44 produces a
voltage that is the average of the two DC input voltages and, as shown in
FIG. 5, may consist of three equal valued resistors R1, R2 and R3. The DC
voltage output of one VCO 48 is connected to one end of R1 and the DC
voltage output of the other VCO 48 is connected to one end of R2. The
other ends of R1 and R2 are connected together and through R3 to ground.
The output of the voltage divider 44, i.e., the junction of R1, R2 and R3
is connected to the VCO 46, which in response to the input voltage
produces a reference signal consisting of a train of pulses having a
frequency that is the average of the two synchronized signals namely,
.alpha.(f.sub.14 +f.sub.16)/2. The reference signal produced by the VCO 46
and the synchronized signals produced by the phase-locked loops 32 and 38
are all applied to the phase differentiator 42. Based upon these input
signals the phase differentiator 42 determines the phase differences
.phi..sub.14 and .phi..sub.16. In place of the phase difference .phi., the
phase differences .phi..sub.14 and .phi..sub.16 are applied to the
controller 26 and output system 28. The reference signal produced by the
VCO 46 is applied to the input system 24, the controller 26, and the
output system 28 in place of the synchronized signal produced by the
phase-locked loop 32. The controller then functions in accordance with
equations (6) and (7) and the previous description.
The apparatus shown in FIG. 5 can be modified to support more than two
repetitive vibration sources. For example, if there were a third
repetitive vibration source, the DC voltage produced by the phase-locked
loop associated with the third source would also be applied to the voltage
divider, and the voltage divider would produce a voltage that is the
average of the three DC voltages, which would be applied to the VCO 46.
Also, the resistances of the voltage divider 44 could be chosen so that
the reference signal produced by the VCO 46 has a frequency other than the
average of the frequencies of the synchronized signals.
While the preferred embodiment of the invention has been illustrated and
described, it will be appreciated that various changes, in addition to
those previously mentioned herein, can be made therein without departing
from the spirit and scope of the invention. For example, the step of
forming the subset B shown in FIG. 4A could be eliminated and then all the
frequency components of set S would be processed for each actuator as
shown in FIG. 4B. Further, while the preferred embodiment of the invention
has been described as an improvement to the prior art frequency-domain
vibration controller disclosed in U.S. patent application Ser. No.
07/575,223, the improvements disclosed herein could be applied to other
frequency-domain vibration controllers. Thus, the invention can be
practiced otherwise than as specifically described therein.
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